Periodic homogenization of non-local operators with a convolution type\n kernel

2016/04/18 by Andrey Piatnitski, Piatnitski, Andrey, Е. Г. Жижина +1 · 2 citations
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Differential Equations and Numerical Methods #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Mathematical Physics (math-ph) #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1604.05038

openalex publication_date 2016/04/18 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

The paper deals with homogenization problem for a non-local linear operator\nwith a kernel of convolution type in a medium with a periodic structure. We\nconsider the natural diffusive scaling of this operator and study the limit\nbehaviour of the rescaled operators as the scaling parameter tends to 0. More\nprecisely we show that in the topology of resolvent convergence the family of\nrescaled operators converges to a second order elliptic operator with constant\ncoefficients. We also prove the convergence of the corresponding semigroups\nboth in L² space and the space of continuous functions, and show that for\nthe related family of Markov processes the invariance principle holds.\n

Cited by

• Homogenization of non-symmetric convolution type operators
• Homogenization of parabolic problems for non-local convolution type operators under non-diffusive scaling of coefficients

Related

• Homogenization of non-autonomous operators of convolution type in periodic media
• Homogenisation and spectral convergence of high-contrast convolution type operators
• Homogenization of biased convolution type operators
• Periodic homogenization of convolution type operators with heavy tails
• Homogenization of nonlocal spectral problems